I think everyone is different. I had a back to back labour and was also induced (I ended up with a csection but I did get to 10cm and was pushing before this happened so know what contractions are like but don't know about the pain of actually pushing the baby out) Hoping to find out this time around.
When I went into hospital at 39+4 to be induced I was checked and was 4cm already and I didn't even know about it, had no pain just tummy tightenings. Once I was given the drip to make my contractions quicker and my waters were burst the pain was worse, mine was more in my back because of the way my son was lying though. It was similar to bad period pains and an uncomfortable tighting, I think its a similar feeling to when you get bad cramp in your calf, I didn't find it too unbearable though it is just really tiring and started to get on my nerves after a while.
My friend went for a routine midwife appointment when she was 1 week overdue and the midwife was going to do a sweep and when she checked she was already 6cm and in labour and she had been walking around fine all day and was only feeling very slight discomfort and didn't think they were contractions at all. She went to hospital and was only in pain for 30 minutes before her daughter was born, and she was a good size 8lb 3. So guess everyone is different.